The potential impact of quantum information
science (QIS) on large-scale computing is tantalizing due to the capability to
manipulate 2^N complex numbers where N is the number of qubits. Even for N=60, one approaches exascale.
Additionally, Moore’s law scaling, nearing 5 nm scale, is approaching physical
limits. Present day experimental quantum computers are very modest in terms of
size and general capability. Whether they may someday be useful for large-scale
computation is unknown due to fundamental constraints. Efficient operations are linear. Copying data is approximate. Measurement, or obtaining output is
expensive. Here we present two research areas where QIS and plasma theory
overlap in interesting ways: 1) quantum algorithms solving the Vlasov equation,
and 2) direct numerical simulation of ultra-cold non-neutral ion plasmas used
in QIS. We have developed a quantum
algorithm that time evolves the linear Vlasov equation with an exponential speed up, thereby, directly addressing the computational
demands of the 6D phase space. Progress
is being made on developing strategies for the nonlinear problem. A series expansion with good convergence
properties using the Homotopy Analysis method (HAM)[1] allows formulation of
the nonlinear problem as a large number of matrix multiplies suitable for an
efficient quantum algorithm.
Additionally, we will discuss how plasma theory can help support QIS via
many-particle simulation of ultra-cold non-neutral ion plasmas. A Penning trap is being used to simulate
100’s of interacting quantum spins using an ultracold 2D crystal of singly-ionized
Beryllium ions[2]. The simulation
obtains excellent agreement with linear eigenmode analysis and includes a
fairly detailed laser doppler cooling model that allows prediction of the
ultracold plasma steady state, and shows agreement with experimentally observed
temperatures.